|
|
Re: Vindication of Goldbach's conjecture
Posted:
Jun 22, 2012 8:30 PM
|
|
On Jun 22, 11:14 am, mluttgens <lutt...@gmail.com> wrote:
> On 22 juin, 13:05, Gus Gassmann <horand.gassm...@googlemail.com>
> wrote:
>
>
>
>
>
>
>
>
>
> > On Jun 22, 7:40 am, mluttgens <lutt...@gmail.com> wrote:
>
> > > On 22 juin, 03:19, Gus Gassmann <horand.gassm...@googlemail.com>
> > > wrote:
>
> > > > On Jun 21, 7:29 pm, mluttgens <lutt...@gmail.com> wrote:
>
> > > > > For N = 1000000, one gets 10804 Goldbach's pairs.
> > > > > The relation between log N and log n is log n = 0.727*log N -0.436
>
> > > > Note that this is not an equation, as it is not satisfied for N = 4.
>
> > > The linear relation has been calculated from N = 50 to N = 1000000.
> > > Using it, one gets n = 8433 when N = 1000000, which is less than the
> > > exact value 10804.
> > > With the help of a graph, one could infer that another relationship,
> > > probably exponential, would be more appropriate. This would of course
> > > still clearer vindicate Goldbach's conjecture.
>
> > You chose not to respond to my main substantive point, which was that
> > vindication =/= proof. Evidence in favor of the conjecture is hardly
> > news. After all, the original conjecture was based on at least some
> > evidence, so you are approximately 270 years too late. And since n(N),
> > the number of ways one can partition N into primes, is not monotonic*,
> > you cannot rule out a situation where N > 2 and n(N) = 0.
>
> > * n(8) = n(12) = 1, but n(10) = 2.
>
> And n(38) = 3, but you cannot find an even number N such as n(N) = 0!
>
> Why don't you react more positively instead of quibbling about the
> meaning of proof.
>
> During those 270 years, nobody tried to correlate log N with log n.
Of course they have. Did you not even open up that wikipedia article I
cited for you?
> If I had big computing power, I'd try numbers N =
> 10^2, 10^3, etc... till for instance 10^15, and determine more
> precisely the
> curve linking the two logs.
> If such curve confirms the positive correlation I found, it would not
> only vindicate,
> but also *prove* the validity of Goldbach's conjecture.
No, it would not. Unless you can show that the error in your formula
is such that n is bounded away from zero, you have nothing.
Vindication of the Goldbach conjecture is cheap, and it has been
around for 270 years. A *proof* is elusive, and there one could make a
definite name for oneself. First thing, of course, would be to
acknowledge and understand the contributions of other, prior
researchers.
YMMV.
|
|
